Locked and unlocked polygonal chains in 3D
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Folding and Unfolding in Computational Geometry
JCDCG '98 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Folding and Unfolding Linkages, Paper, and Polyhedra
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
Chain Reconfiguration. The INs and Outs, Ups and Downs of Moving Polygons and Polygonal Linkages
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
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This paper considers reconfigurations of polygons, where each polygon edge is a rigid link, no two of which can cross during the motion. We prove that one can reconfigure any monotone polygon into a convex polygon; a polygon is monotone if any vertical line intersects the interior at a (possibly empty) interval. Our algorithm computes in O(n2) time a sequence of O(n2) moves, each of which rotates just four joints at once.